The error is the same in both instances (thatís where the 1.96 comes from).
In the first equation the analyst is expecting the difference between the means to be about 0.05 (10% of the size of the standard deviation =0.5), in the second equation the analyst is anticipating the difference between means to be greater (20% of the size of the standard deviation) and thus can use a smaller sample size for the same degree of error.